View source for Physics/Synopsis

==[[Physics]]==
==[[Force]]==
:{|width=90%
|-
| '''Force '''
| '''Symbol'''
| '''Mathematical Formula'''
|-
| Opposing Force
| <math>F_-</math> 
| <math>-F</math>
|-
| Gravity Force
| <math>F_g</math> 
| <math>G \frac{Mm}{r^2}</math>
|-
| Motion Force
| <math>F_a</math> 
| <math>m a = m \frac{v}{t} = \frac{p}{t}</math>
|-
| Pressure Force
| <math>F_A</math> 
| <math>\frac{F}{A}</math>
|-
| Elastic Force
| <math>F_x</math> 
| <math>-k x</math>
|-
| Circulation Force
| <math>F_r</math> 
| <math>mvr=pr</math>
|-
| Centripetal Force
| <math>F_c</math> 
| <math>m\frac{v^2}{r}</math>
|-
| Electrostatic Force
| <math>F_q</math> 
| <math>\frac{q_+ q_-}{r^2}</math>
|-
| Electromotive force
| <math>F_E</math> 
| <math>qE</math>
|-
| Electromagnetomotive Force
| <math>F_B</math> 
| <math>\pm qvB</math>
|-
| Electromagnetic Force
| <math>F_{EB}</math> 
| <math>q(E \pm vB)</math>
|}

==[[Motion]]==
===Linear Motion===
: O ----> O

:{|width=80%
|- 
| Distance || <math>s</math> || <math>vt </math>
|-
| Time || <math>t</math> || <math>t</math>
|-
| Speed || <math>v</math> || <math>\frac{s}{t} </math>
|-
| Accelleration || <math>a</math> || <math>\frac{v}{t} </math>
|-
| Force || <math>F</math> || <math>m \frac{v}{t}</math>
|-
| Work || <math>W</math> || <math>F s</math>
|-
| Energy || <math>E</math> ||<math>\frac{W}{t}</math>
|-
|}


: O
: ↓
: O

:{|width=70%
|-
| Distance || <math>s</math> || <math>h </math>
|-
| Time || <math>t</math> || <math>t</math>
|-
| Speed || <math>v</math> || <math>\frac{h}{t} </math>
|-
| Accelleration || <math>a</math> || <math>\frac{h}{t^2} </math>
|-
| Force || <math>F</math> || <math>m g</math>
|-
| Work || <math>W</math> || <math>m g h</math>
|-
| Energy || <math>E</math> ||<math>\frac{m g h}{t}</math>
|-
|}

* [[ Non-Uniform linear motion]]
:{|width=100%
|-
| Distance || <math>s</math> || <math>(v_o + at)t </math>
|-
| Time || <math>t</math> || <math>t</math>
|-
| Speed || <math>v</math> || <math>v_o + at </math>
|-
| Accelleration || <math>a</math> || <math>\frac{\Delta v}{\Delta t}</math>
|-
| Force || <math>F</math> || <math>m \frac{\Delta v}{\Delta t}</math>
|-
| Work || <math>W</math> || <math>F t (v_o+at)</math>
|-
| Energy || <math>E</math> ||<math>F (v_o+at)</math>
|-
|}

===[[Non Linear Motion]]===
:{|width=100%
|-
| Distance || <math>s(t)</math>||<math>\int v(t) dt</math>
|-
| Time || <math>t</math> || <math>t</math>
|-
| Speed || <math>v(t)</math>||<math>v(t)</math>
|-
| Acceleration ||<math>a(t)</math>||<math>\frac{d}{dt}v(t)</math>
|-
| Force ||<math>F(t)</math> || <math>m \frac{d}{dt}v(t)</math>
|-
| Work ||<math>W(t)</math> || <math>F \int v(t) dt</math>
|-
| Energy ||<math>E(t)</math> || <math>\frac{F}{t} \int v(t) dt</math>
|-
|-
|}

===Circular Motion===
:[[File:Circle-withsegments.svg|150px]][[File:Uniform_circular_motion.svg|200px]][[File:Velocity-acceleration.PNG|200px]]
* [[Complete full circle]]
:{|width=100%
|-
| Distance || <math>s</math> || <math>2 \pi r</math>
|-
| Time|| <math>t</math> || <math>t</math>
|-
| Speed ||  <math>v</math> || <math>r \frac{2 \pi}{t} = r \omega</math>
|-
| Acceleration||  <math>a</math> || <math>\frac{r \omega}{t}</math>
|-
| Angular spped  ||  <math>\omega</math> || <math>\frac{2 \pi}{t} = 2 \pi f = \frac{v}{r}</math>
|-
| Frequency || <math>f</math> || <math>\frac{1}{t}</math> 
|-
| Force || <math>F</math> || <math>m \frac{r \omega}{t}</math>
|-
| Work || <math>W </math> || <math>p r \omega</math>
|-
| Energy || <math>E</math> || <math>\frac{p r \omega}{t}</math>
|}

* [[Circle's arc ]]
:{|width=80%
|-
| Distance || <math>s</math> || <math>r \theta</math>
|-
| Time|| <math>t</math> || <math>t</math>
|-
| Speed ||  <math>v</math> || <math>r \frac{\theta}{t} </math>
|-
| Acceleration||  <math>a</math> || <math>\frac{r \theta}{t^2}</math>
|-
| Force || <math>F</math> || <math>m \frac{r \theta}{t^2}</math>
|-
| Work || <math>W </math> || <math>p r \frac{\theta}{t} </math>
|-
| Energy || <math>E</math> || <math>\frac{p r \theta}{t^2}</math>
|}

===[[Momentum]]===
====Characteristics====
:<math>F = m a = m \frac{v}{t} = \frac{p}{t} </math>
:<math>p = m v = F t </math>

====[[Momentum of a mass]]====
:{|width=80%
|-
| Speed ||  <math>v</math> || <math>v </math>
|-
| Mass||<math>m</math> || <math>m </math>
|-
| Momentum || <math>p</math> || <math>m v = F t</math> 
|-
| Force || <math>F</math> || <math>m a = m \frac{v}{t} = \frac{p}{t}</math>
|-
| Work || <math>W</math> || <math>F s = F v t = p v</math>
|-
| Energy || <math>E</math> || <math>F v = F a t = p a</math>
|-
|}

==== [[Momentum of a relativistic mass]]====
:{|width=80%
|-
| Speed ||  <math>v</math> || <math>\gamma = \sqrt{1 - \frac{v^2}{C^2}} </math>
|-
| Mass||<math>m</math> || <math>m_o(\gamma-1) </math>
|-
| Momentum || <math>p</math> || <math>m v </math> 
|-
| Energy || <math>E</math> || <math>pv</math>
|-
|}

====[[Momentum of a massless quanta]]====
:{|width=100%
|-
| Speed ||  <math>v</math> || <math>C = \lambda f </math>
|-
| Mass||<math>m</math> || <math>h = p \lambda </math>
|-
| Energy || <math>E</math> || <math>pv = pC=p \lambda f = h f</math>
|-
| Momentum || <math>p</math> || <math>\frac{h}{\lambda}</math> 
|-
| Wavelength || <math>\lambda</math> || <math>\frac{h}{p} = \frac{C}{f}</math> 
|-
|}

==== [[Momentum of an electric charge in circle]]====
:{|width=70%
|-
| Equilibrium || <math>QvB = p \frac{v}{r}</math>
|-
| Speed ||  <math>v = \frac{Q}{m}Br</math>
|-
| Radius ||  <math>r = \frac{p}{QB}</math>
|}

====[[Momentum of atom's free electron]]====
:{|width=100%
|-
| Equilibrium || <math>hf=hf_o+\frac{1}{2} m v^2</math>
|-
| Speed ||  <math>v = \sqrt{\frac{2}{m}(hf-hf_o)} = \sqrt{\frac{2}{m}(nhf_o)}</math><br>With<br><math>f > f_o = nf_o</math> to have <math>v>0</math>
|-
|}

==== [[Momentum of a bind electron]]====
:{|width=100%
|-
| Equilibrium || <math>nhf=mvr 2\pi</math>
|-
| Speed ||  <math>v = \frac{1}{2 \pi} \frac{nhf}{mr}</math>
|-
| Radius ||  <math>r = \frac{1}{2 \pi} \frac{nhf}{mv}</math>
|-
| Potential Energy Level n || <math>n = 2 \pi \frac{mv}{hf}</math>
|-
|}

===[[Wave]]===

====AC electrical sinusoidal wave generator====
An interaction of 2 electromagnets creates an AC electricity that has amplitude varies sinusoidally
: <math>v(t) = A Sin (\omega t + \theta)</math>
:[[File:Alternator_1.svg|200px]]

====LC sinusoidal wave generator====
:[[File:Series_LC_Circuit.svg|100px]]
Series LC operates at equilibrium satisfy wave equation 
:<math>\frac{d^2}{dt^2} i(t) = - \frac{1}{T} i(t)</math>

that has root of a sinusoidal wave function
:[[File:FreqWave1.png|200px]]
:<math>i(t) = A Sin \omega t</math>
: <math>\omega = \sqrt{\frac{1}{T}}</math> 
: <math>T = LC</math>

====Electromagnetic sinusoidal wave generator====
:[[File:VFPt_Solenoid_correct2.svg|200px]]
A coil of N turns operates at equilibrium satisfy wave equation 
:<math>\nabla^2 E(t) = - \omega E(t)</math>
:<math>\nabla^2 B(t) = - \omega B(t)</math>

that has root of a sinusoidal wave function
:[[File:Onde_electromagnetique.svg|300px]]
:<math>E(t) = A Sin \omega t</math>
:<math>B(t) = A Sin \omega t</math>

: <math>\omega = \sqrt{\frac{1}{T}} = C = \lambda f</math> 
: <math>T = \mu \epsilon</math>

====Wave Characteristics====
:{|width=70%
|-
| Distance || <math>s</math> || <math>\lambda</math>
|-
| Time|| <math>t</math> || <math>t</math>
|-
| Speed ||  <math>v</math> || <math>\frac{\lambda}{t} </math>
|-
| Angular speed||<math>\omega</math> || <math>2 \pi f </math>
|-
| Frequency || <math>f</math> || <math>\frac{1}{t}</math> 
|-
| Sinusoidal wave equation || <math>f^{''}(t)</math> || <math>- \omega f(t)</math> 
|-
| Sinusoidal wave function || <math>f(t)</math> || <math>A Sin \omega t</math> 
|}

====Wave types====
:{|width=100%
|-
| Wave || 2 dimensional sinusoidal wave || 3 dimensional sinusoidal plane wave 
|-
|  || [[File:FreqWave1.png|200px]] || [[File:Onde_electromagnetique.svg|300px]] 
|-
| Wave oscillation equation || <math>\frac{d^2}{dt^2} f(t) = -\omega f(t)</math> 
|-
| Wave function || <br><math>f(t) = A Sin \omega t</math> || <br><math>E(t) = A Sin \omega t</math><br><math>B(t) = A Sin \omega t</math><br><math>\omega = \sqrt{\frac{1}{T}} = C = \lambda f</math><br><math>T = \mu \epsilon</math>
|-
|}

==[[Electricity]]==
===Electricity Types===
:{|width=100%
|-
|'''Electricity types ''' || '''Definition ''' || '''Mathematical Formula ''' || '''Source'''
|-
| [[DC Electricity]] ||  Electricity that provides constant voltage over time || <math>v(t) = V</math> || [[Electrolysis]], [[Electrochemcial Cell]], [[PhotonVoltaic]]
|-
| [[AC Electricity]] || Electricity that provides sinusoidal changing voltage over changing time || <math>v(t) = V Sin \omega t</math> || [[Electromagnetic induction]]
|-
|}

===DC & AC Response===
* [[Resistor circuit]]
:{|width=80% 
|-
| '''Characteristics'''|| '''DC''' || '''AC'''
|-
| Voltage || <math>V = I R</math> || <math>v = i R</math> 
|-
| Current || <math>I =\frac{V}{R}</math> || <math>i =\frac{v}{R}</math> 
|-
| Resistance || <math>R = \frac{V}{I}</math> || <math>R = \frac{v}{i}</math>
|-
| Power provided || <math>P_V = I V </math> || <math>P_V = i v </math>
|-
| Power Loss || <math>P_R = I^2 R(T) = \frac{V^2}{R(T)}</math> ||  <math>P_R = i^2 R(T) = \frac{v^2}{R(T)}</math>
|-
| Power delivered|| <math>P = P_V - P_R</math>
|-
| Reactance || || <math>X_R=0</math>
|-
| Impedance || || <math>Z_R = X_R + R = R</math>
|-
| Phase || || <math>0</math>
|-

|}

* [[Capacitor circuit]]
:{|width=100% 
| '''Characteristics'''|| '''DC''' || '''AC'''
|-
| Voltage || <math>V = Q C = \frac{W}{Q}</math> || <math>v = \frac{1}{C} \int i dt</math>
|-
| Charge || <math>Q = \frac{V}{C}</math>
|-
| Capacitance|| <math>C = \frac{V}{Q}</math>
|-
| Current || <math>I = \frac{Q}{t}</math> || <math>i = C \frac{dv}{dt}</math> 
|-
| Power provided || <math>P_V =  I V = (\frac{Q}{t}) (\frac{W}{Q}) = \frac{W}{t}</math> ||<math>p = \frac{1}{2} Cv^2</math> 
|-
| Reactance || || <br><math>X_C(t) = \frac{v}{i}</math> <br><math>X_C(j \omega) = \frac{1}{j \omega C}</math> <br><math>X_C(\omega \theta) = \frac{1}{\omega C} \angle -90</math>
|-
| Impedance || || <br><math>Z_C(t) = X_C + R_C</math> <br><math>X_C(j \omega) = \frac{1}{j \omega C} + R_C </math><br><math>X_C(\omega \theta) = \frac{1}{\omega C} \angle -90 + R \angle 0 </math>
|-
| Phase || ||<math>Tan \theta = \frac{1}{\omega T}</math>
|-
| Time Constant || || <math>T = CR_C</math>
|-
|}

* [[Inductor circuit]]
:{|width=80% 
|-
| '''Characteristics''' || '''DC''' || '''AC'''
|-
| Magnetic Field Strength || <math>B = L I</math>
|-
| Current || <math>I = \frac{B}{L}</math>
|-
| Inductance || <math>C = \frac{B}{I}</math>
|-
| Current || <math>I = \frac{Q}{t}</math>
|-
| Power provided || <math>P_V = I V = (\frac{B}{l}) (\frac{W}{Q}) = \frac{W}{t}</math> || 
|-
| Reactance || || <br><math>X_L(t) = \frac{v}{i}</math> <br><math>X_L(j \omega) = j \omega L</math> <br><math>X_L(\omega \theta) = \omega L \angle 90</math>
|-
| Impedance || || <br><math>Z_C(t) = X_C + R_C</math> <br><math>X_C(j \omega) = j \omega L + R_L </math><br><math>X_C(\omega \theta) = \omega L \angle 90 + R \angle 0 </math>
|-
| Phase || ||<math>Tan \theta = \omega T</math>
|-
| Time Constant || || <math>T = \frac{L}{R_L}</math>
|-
|}

* [[Electric Decay]]
:{|width=100%
|-
| [[File:RL_Series_Open-Closed.svg|80px]] || <br><math>\frac{d}{dt} i = -\frac{1}{T} i</math> || <br><math>i = A e^{-\frac{1}{T} t}</math> || ||<math>T=\frac{L}{R}</math> 
|-
| [[File:RC_switch.svg|80px]] || <br><math>\frac{d}{dt} v = -\frac{1}{T} v</math> || <br><math>v = A e^{-\frac{1}{T} t}</math> || ||<math>T=RC</math> 
|}

* [[Electric Oscillation]]
:{|width=100%
|-
| '''Modes of Oscillation'''|| '''Oscillation equation''' || '''Wave Function''' || '''Angular Speed''' || '''Oscillation Time Constant''' || '''Oscilation Constant''' || '''Decay Constant '''' || '''Decay Time Constant'''
|-
| Electric decay current <br>sinusoidal wave oscillation <br>[[File:RLC_series_circuit_v1.svg|80px]] || <math>\frac{d^2}{dt^2} i = -2\alpha\frac{d}{dt}i - \beta i</math> || <math>i = A(\alpha) Sin \omega t</math> ||<math>\omega=\sqrt{\beta - \alpha}</math> || <math>T=LC</math> || <math>\beta=\frac{1}{T}</math>|| <math>\alpha=\beta \gamma</math>|| <math>\gamma= RC</math>
|-
| Electric peak current <br>sinusoidal wave oscillation <br>[[File:RLC_series_circuit_v1.svg|80px]] || <br><math>Z_L = - Z_C</math><br><math>Z_t = R</math> || <br><math>i(\omega=0)=0</math><br><math>i(\omega=\omega_o)=\frac{v}{2}</math><br><math>i(\omega=00)=0</math> || <math>\omega_o =\sqrt{\frac{1}{T}}</math>|| <math>T=LC</math>
|-
| Electric current <br>sinusoidal wave oscillation<br>[[File:Series_LC_Circuit.svg|80px]]  || <br><math>\frac{d^2}{dt^2} i = -\frac{1}{T} i</math> || <math>i = A Sin \omega t</math> ||<math>\omega=\sqrt{\frac{1}{T}}</math> || <math>T=LC</math> 
|-
| Electric current sinusoidal <br>standing wave oscillation<br>[[File:Series_LC_Circuit.svg|80px]]  || <br><math>Z_L = - Z_C</math> || <math>V_L = - V_C</math> || <math>\omega_o=\sqrt{\frac{1}{T}}</math> || <math>T=LC</math>
|-
|}

==Electromagneticism==
===Electric charge===
:{|width=100%
|-
| '''Charge acquired process''' || '''Electric charge''' || '''Charge quantity''' || '''Electric field''' || '''Magnetic field'''
|-
| Matter + e<sup>-</sup> || - || -Q || -->E<-- || B ↓
|-
| Matter - e<sup>-</sup> || + || +Q || <--E--> || B ↑
|-
|}

===Electromagnetic force===
:{|width=100%
|-
| '''Force''' || '''Symbol''' || '''Mathematical formula''' 
|-
| Electrostatic Force || <math>F_q</math> || <math>K \frac{q_+ q_-}{r^2}</math>
|-
| Electromotive Force || <math>F_E</math> || <math>q E</math>
|-
| Electromagnetomotive Force || <math>F_B</math> || <math>\pm q v B</math>
|-
| Electromagnetic Force || <math>F_{EB}</math> || <math>qE \pm q vB = q(E\pm B)</math>
|}

===Electromagnetic Field ===
:{|width=100%
|-
| '''Configuration ''' || '''Symbol ''' || '''Mathematical Formulas'''
|-
| For any configuration  || <math>B</math> || <math>B = L I</math>
|-
| For straight line conductor || <math>B</math> || <math>B = L I = \frac{\mu}{2 \pi r} I</math> || Circular B field
|-
| For circular loop conductor || <math>B</math> || <math>B = L I = \frac{\mu}{2 r} I</math> || Circular B field around a point charge
|-
| For coil of N  circular loops conductor ||  <math>B</math> || <math>B = L I = \frac{N \mu}{l} I</math> || Eleptic B field around the coil
|-
|}

===Electromagnetic Principles===
:{|width=100%
|-
| || ||[[File:VFPt_Solenoid_correct2.svg|200px]]
|-
| Electromagnetic field  || <br><math>B</math> || <br><math>L I</math>
|-
| Induced electromagnetic field   ||<br><math>\phi</math> ||<br> <math>-NB=-NLI</math>
|-
| Electromagnetization field ||<br><math>H</math> || <br><math>\frac{B}{\mu} = \frac{\phi}{N\mu}</math>
|-
| [[Eletromagnetization]] ||<br> || <br><math>\nabla \cdot D = \rho</math><br><math>\nabla \times E = -\nabla B</math><br><math>\nabla \cdot B = 0</math><br><math>\nabla \times H = J + \nabla B</math>
|}
:{|width=90%
|-
| Coil's voltage induction intencity  || <br><math>V</math> || <br><math>V = \frac{dB}{dt} = L \frac{dI}{dt}</math>
|-
| Turn's induced voltage intencity  || <br><math>\epsilon</math> || <br><math>-\frac{d\phi}{dt}=-N\frac{dB}{dt}=-NL\frac{d}{dt}I</math>
|}


:{|width=80%
|-
| [[Electromagnetic oscillation]] || <br>|| <br><math>\nabla \cdot E = 0</math><br><math>\nabla \times E = \frac{1}{T}</math><br><math>\nabla \cdot B = 0</math><br><math>\nabla \times B = \frac{1}{T}</math>
|-
| [[Electromagnetic  wave]] <br>[[File:Onde_electromagnetique.svg|200px]] || <br>|| <br><math>\nabla^2 E = - \omega E</math><br><math>\nabla^2 B = - \omega B</math><br><math>E =  A Sin \omega t</math><br><math>B =  A Sin \omega t</math><br><math>\omega=\sqrt{\frac{1}{T}}=C=\lambda f</math><br><math>T=\mu \epsilon</math>
|-
| [[Electromagnetic wave radiation]] || <br> || <br><math>v=\omega=\sqrt{\frac{1}{\mu \epsilon}}=C=\lambda f</math><br><math>E=pv=pC=p \lambda f= h f</math><br><math>h=p \lambda</math><br><math>p = \frac{h}{\lambda}</math><br><math>\lambda=\frac{h}{p}=\frac{C}{f}</math>
|}

==Photon ==
[[Photon]] is defined as energy of a massless quanta travels as an electromagnetic oscillation wave radiation at speed equal to speed of light
Mathematical formula of 
: <math> E = hf = \hbar \omega</math> 

Photon exist in 2 states 
: [[Radiant Photon]] at threshold frequency fo
:: <math> E = hf_o = \hbar \omega_o</math> 
: [[Non Radiant Photon]] at frequency greater than threshold frequency fo
::<math> E = hf = \hbar \omega</math> . With f>fo

Photon can only exist in one state at a time . This is Heiseinberg's uncertainty principle the success rate of  finding photon
:<math>\Delta p \Delta \lambda = \frac{1}{2} \frac{h}{2 \pi} = \frac{\hbar}{2}</math>

===Quanta of Photon===
Quantity of photon's energy . Quanta is denoted as '''h''' measured in has a constant value h = 
: <math>h = p \lambda</math> 

Quanta process [[Wave particle duality]] meaning 
: Sometimes it behaves like wave <math>\lambda=\frac{h}{p}</math> 
: Sometimes it behaves like particle <math>p=\frac{h}{\lambda}</math>

===Photon and matter===
Photon and matter interacts to create Heat transfer through 3 phases [[Heat conduction]], [[Heat convection]] and [[Heat radiation]]
:{|width=100%
|-
| '''Heat transfer''' ||  || || 
|-
| '''Heat conduction''' || Matter changes it's temperature while absorb heat energy || <math>\Delta T = T_1-T_0</math><br><math>E=mC \Delta T</math> 
|-
| '''Heat convection ''' || Matter conducts heat energy to the max at Threshold frequency fo ||  <br><math>f_o=\frac{C}{f_o}</math><br><math>E=hf_o</math> 
|-
| '''Heat radiation''' || Matter uses excess energy above maximum absorbing energy to release electron off atom || <br><math>hf-hf_o = \frac{1}{2}m v^2</math>. When v>0 <br><math>v=\sqrt{\frac{2}{m} nhf_o}</math> with f > f<sub>o</sub>
|-
|}

Causes  matter to decay through 3 kinds of decays
:{|width=100%
|-
| '''Mattter decay ''' || '''Reaction ''' || 
|-
| [[Alpha decay]] || Ur--> Th - He + Alpha radiation || 
|-
| [[Beta decay]] || C-->N + Beta radiation 
|-
| [[Gamma decay]] || ee) + Gamma radiation
|}

Experiment has shown that, electron of an atom can be freed or binded from absorbing or releasing photon's energy 
:{|width=100%
|-
| '''Atom decay ''' || '''Absorbing photon energy ''' || '''Releasing photon energy '''
|-
| Equilibrium  || <math>hf = hf_o + \frac{1}{2} m v^2</math> || <math>nhf=mvr 2 \pi</math>
|-
| v || <math>\sqrt{\frac{2}{m}(hf-hf_o)}=\sqrt{\frac{2}{m}(nf_o)}</math>|| <math>\frac{1}{2 \pi} \frac{nhf}{mr}</math>
|-
| r || || <math>\frac{1}{2 \pi} \frac{nhf}{mv}</math>
|-
| n || || <math>2 \pi \frac{mv}{hf}</math>
|-
|}

[[Category:Physics]]